Was the fall of Rome inevitable?

There is tremendous scholarly debate on this very
question; particularly in the last few years. The major factor in the fall of Rome was,
of course, the Barbarian migrations. ("Barbarian" was a term originating with the
Greeks, who said that the language of the German tribes sounding like the sounds of
sheep.) The Roman Empire had grown so large that it's borders were tremendous, and
difficult to patrol. Now, let's muddy the water a bit. In the year 376 (one hundred
years before the end of Empire) the Romans allowed the Goths to cross over to escape
from the oncoming Huns. This in essence opened Pandora's box. The Goths continued to
stream over, and occupied Roman lands. Needless to say, they did not pay Roman taxes,
which reduced the Empire's income. The Huns themselves were a factor. The Romans had a
tenuous relationship with the Huns under Attila, which mainly consisted of the Romans
buying them off.

Then there was internal strife within the
Empire. Roman armies, since Julius Caesar, were loyal to their commander, who typically
(but not always) was the Emperor. (Another little known factor: the Emperor himself was
known as the "Augustus," his successor as the "Caesar.") During a time of dissension,
there were as many as four claimants to the throne, all supported by their troops. Out
of 27 Emperors, only one actually died of natural causes. The others were either
murdered or committed suicide.

To muddy the water even
further; Germanic tribes often fought in the Roman Armies as mercenaries. They often
sided with one General or another, generally with the highest bidder. Finally, when a
General named Orestes installed his son (a feeble minded teenager) as Emperor, (Romulus
II Augustulus) the Germanic General Odoacher put an end to the nonsense by having
Orestes put to death, and forcing Romulus to abdicate. He then forwarded the crown and
purple robe of the Emperor to the Emperor in Constantinople with a letter that he was
the sole Roman Emperor now.

So, the variables would be
internal dissension, Germanic migrations (invasion is probably too strong a word) the
pressure created by the Huns, and the sheer size of the Empire. Could it have been
prevented? Probably, but to do so, the process would have had to be modified at least
100 years before the actual collapse.

Several excellent
sources you might consider: Adrian Goldsworthy: How Rome Fell, Death of a
Superpower; and also Christopher Kelly, The End of Empire: Attila
the Hun and the Fall of Rome.

Verify that f(x) = 2x/( k(k + 1)) for x = 1, 2, 3, . . . ,k can serve as the probability distribution of a random variable in a given range

If f(x) = 2x/k(k+1), x= 1, 2, 3,
4,....k.

To verify whether this is probability distribution
function, we should prove that {Sum f(x) over x = 1, 2, 3, 4,...k} =
1.

x takes a discrete value. That is x takes values like
 x= 1, 2, 3, 4, ......, k.

Let X be the random
variable

f(X =x) = 2x/k(k+1) = 2x/k(k+1), x= 1, 2, 3,
4....k.

Total frequency = {Sum f(X = x) , x= 1, 2, 3,
...n.} =
2*1/k(k+1)+2*2/k(k+1)+2*3/k9k+1)...2*k/k(k+1).

{Sum f(X =
x) , x= 1, 2, 3, ...n.} =
{2/k(k+1)}{1+2+3+..........k}

{Sum f(X = x) , x= 1, 2, 3,
...n.} = {2/k(k+1)}{Sum of the k natural numbers starting from
1}.

{Sum f(X = x) , x= 1, 2, 3, ...n.} =
{2/(k(k+1)}{k(+1)/2}

{Sum f(X = x) , x= 1, 2, 3, ...n.} =
1..

Therefore f(x) is a frequency density function. Or f(x)
is a probability distribution function.

What does "Bicameral Legislature" mean?

A bicameral legislature is one that is split up into two
houses.  Many legislatures around the world are split in this way.  For example, the
Congress of the United States is split up between the House of Representatives and the
Senate.

Bicameral legislatures are generally set up as a
way of providing checks and balances in a governmental system.  In a bicameral system
like that of the US, proposed bills must pass both houses of the legislature before they
can become law.  This makes it harder to pass legislation than it would be in a
unicameral (only one house of the legislature) system.

Determine if the line y+x-2 = 0 and the line 6y-3x +8 = 0 are parallel, perpendicular, or neither.

Given the lines:

y + x -2 =
0

6y-3x + 8 =0

We need to
determine the relation between the lines ( parallel, perpendicular, or
neither)

First we will use the slope to find the
relation.

If the slopes are equal, then the lines are
parallel.

if the product of the slopes is -1, then the
slope are perpendicular.

Let us rewrite the equations of
the lines into the slope form.

==> y = -x + 2
............(1)

==> y = (3/6)x -
8/6

==> y= (1/2)x -
4/3........(2)

We notice that the slopes are not equal.
then the lines are not parallel.

Also, the product of the
slopes is -1*1/2 = -1/2 , then the lines are not
perpendicular.

Then the slopes are not
parallel nor perpendicular.

In Book 13 of The Odyssey, why does Athena test Odysseus?

I think there are two elements two think about in
answering this question. Firstly, the gods in both The Iliad and The Odyssey are shown
to be quite a fickle group, using their human heroes to champion their petty squabbles
against other gods and treating them as playthings. Thus, in a sense, Athena can test
her hero because she is a goddess and she can do what she
likes.

However, also, it is important to remember what kind
of character Odysseus is. He is not known as "the wily Odysseus" for nothing, and
certainly throughout the rest of the book disguise, deception and illusion are used
readily and frequently to trick, beguile and deceive. Thus, there is something fitting
in Odysseus not realising he has reached Ithaca in this book: the deceiver is himself
deceived. Of course, once Odysseus realises his location, he immediately determines to
employ deception to achieve his goal until the grey-eyed goddess Athena reveals truth
through her own act of self-revelation.

What are some quotes that reflect images of sight/blindness, animals, and hell/demons from the play Othello?

One of the first, and a relatively famous animal quote is
from Iago as he calls up to Brabantio's house in the middle of the night in reference to
his daughter being with Othello: "Even now, no, very now, an old black ram Is tupping
your white ewe."  Of course he is trying to make the image as repellant as possible to
arouse anger in Brabantio and drive him to attack Othello the moor.  Just a little bit
later he says againto Brabantio:

readability="9">

you'll have your daughter covered with a Barbary
horse, you'll have your nephews neigh to you, you'll have coursers for cousins, and
jennets for germans.

Pretty
nasty stuff!

A quote close by that reflects the idea of
vision or blindness is from the First Senator after the Duke asks him how it is possible
that the Turkish preparation makes for Rhodes rather than for Cyprus:  "'Tis a pageant
to keep us in false gaze" reflecting the idea that they have been looking the wrong
way.

How does my fake journal entry I wrote for Chris McCandless fit Chapter 16 of Into the Wild?My assignment was to write a poem, journal entry, or...

I like this initial response, and I think you have come up
with a number of great ideas. Here are a few more ideas to help you develop this
assignment and get an even better mark. You might want to develop what specifically
Chris learnt from his months of solitude and how he has changed as a result. It was
always his intention and dream to stay for longer in Alaska, so you need to explain
fully why he chose to attempt to leave earlier. You might even have him thinking about
some of the many characters he met along the way and thinking about those relationships
and how important they are to him, as he realises it
now.

Lastly, I would write a lot more about what Chris felt
and experienced when he tries to leave and can't. Would he berate himself for not
realising the impact of sping on the ice in Alaska? How would he feel? We are told later
by the author of this great book that if he had a map, he would have realised that he
could have crossed the river in another location, very close to where he was. Would he
wish that he had taken a map? I guess that having decided to make such a big decision,
and then to have that choice taken away from him, is going to make Chris feel upset,
frustrated and annoyed. You need to try and capture that in his
feelings.

Good luck, though! This is a great start and by
considering my questions you should be able to get a good grade.